If $a= \log \frac{2}{3}, b=\log \frac{3}{5}$and $c= 2 \log \sqrt{\frac{5}{2}}$ find the value of: $5^{a+b+c}$

If $x=\log \frac{3}{5},\hspace{0.17em}y=\log \frac{5}{4} and z=2\log \frac{\sqrt{3}}{2}$, find the values of

$x+y-z.$

If $x=\log \frac{3}{5},\hspace{0.17em}y=\log \frac{5}{4} and z=2\log \frac{\sqrt{3}}{2}$, find the value of $3^{ x+y-z.}$

If $x=lo{g}_{10}12,\hspace{0.17em}y=lo{g}_{4}2\times lo{g}_{10}9$ and $z=lo{g}_{10}0.4,$ find the value of$x-y-z.$

If $x=lo{g}_{10}12,\hspace{0.17em}y=lo{g}_{4}2\times lo{g}_{10}9$ and $z=lo{g}_{10}0.4,$ find the value of $7^{ x-y-z}$

Express ${\log }_{10}2+1$ in the form of ${\log }_{10}x$.